Remember to also check the sources linked at the bottom of this post. If you check my jslife moving objects update you will find that the (2,0)c/10 you posted is the smallest by bounding box, but not by minimum population:

I'm not exactly sure what the smallest (2,0)c/12 ship is. All known (2,0)c/12 ships are based on the reaction posted here. The forward domino-spark ship can be placed in slightly different phases and positions to create different p12 ships. The Dragons can be moved to reduce the bounding box, but this might increase the minimum population:

The difficulty with using HWSSs is the need for four synchronized gliders rather than three for the LWSS or MWSS. A good proof-of-concept construction might be a p136 rake, since periods 124, 128, and 132 have already been achieved. I might try my hand at this project, but I'm not very good with big constructions - especially when they're moving!

Edit: a 100-cell 2c/5 ship that can support the standard B-heptomino tagalong in an unusual way:

The unfortunate thing about this design is that all of the glider turners and duplicators work at p116, but the HWSS synthesis only works at p120 and above. Is there another HWSS synthesis that could allow the p116 rake to be built?

Sokwe wrote:The unfortunate thing about this design is that all of the glider turners and duplicators work at p116, but the HWSS synthesis only works at p120 and above. Is there another HWSS synthesis that could allow the p116 rake to be built?

I'm not sure if it's possible to use this synthesis because of the salvo required, but it does work at p116: